Steffensen's method: Difference between revisions

Plugging <math>x(t)</math> and <math>y(t)</math> into the implicit equation, and writing <math>f(t)</math> as the function whose fixed points are to be found:

fun implicit_equation (x : double, y : double) : double =

(5.0 * x * x) + y - 5.0

fun f (t : double) : double = (* find fixed points of this function *)

let

val x = x_convex_left_parabola (t)

val y = y_convex_left_parabola (t)

in

implicit_equation (x, y) + t

end

What is left to be done is simple, but tricky: use the <code>steffensen_aitken</code> function to find those fixed points.